Before digging into permutations and combinations in R using iteration, I invite you to read my first post. Indeed, I have already:
- covered the difference between permutations (order matters) and combinations (order doesn’t matter)
- shown an example
- counted the number of permutations and combinations
- and implemented the formulas in R
So, permutations and combinations can be generated using iteration or recursion. An iteration is a loop in which we repeat instructions, while a recursion is a function that calls itself to repeat instructions.
In the next sections, we will use r loops to enumerate all the possible subsets of r elements from a given set of n elements in base R. But instead of working directly on the subsets, you can of course store them in a data frame.
Variables assignment
cells = c("neutrophils", "monocytes", "lymphocytes", "eosinophils", "basophils")
n = length(cells)Permutations with repetition
r = 2
for (i in 1:n){
for (j in 1:n){
print(paste(cells[i], cells[j], sep = "-"))
}
}r = 3
for (i in 1:n){
for (j in 1:n){
for (k in 1:n){
print(paste(cells[i], cells[j], cells[k], sep = "-"))
}
}
}Permutations without repetition
r = 2
for (i in 1:n){
for (j in setdiff(1:n, i)){
print(paste(cells[i], cells[j], sep = "-"))
}
}r = 3
for (i in 1:n){
for (j in setdiff(1:n, i)){
for (k in setdiff(1:n, c(i, j))){
print(paste(cells[i], cells[j], cells[k], sep = "-"))
}
}
}Combinations with repetition
r = 2
for (i in 1:n){
for (j in i:n){
print(paste(cells[i], cells[j], sep = "-"))
}
}r = 3
for (i in 1:n){
for (j in i:n){
for (k in j:n){
print(paste(cells[i], cells[j], cells[k], sep = "-"))
}
}
}Combinations without repetition
r = 2
for (i in 1:n){
for (j in setdiff(i:n, i)){
print(paste(cells[i], cells[j], sep = "-"))
}
}r = 3
for (i in 1:n){
for (j in setdiff(i:n, i)){
for (k in setdiff(j:n, c(i, j))){
print(paste(cells[i], cells[j], cells[k], sep = "-"))
}
}
}Conclusion
To sum up, the implementation of the four cases is quite easy in R. Until now, I only had to generate pairs of items without order and without repetition. And you?
